Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
Each serial number of the product consists of six components. First two are letters and remaining four are numbers. So all the serial numbers will look as shown below.
LLNNNN⇑⇑⇑⇑⇑⇑6510987
For the first position of serial number we can have one of the 6 letters. As repetition is not allowed first position of serial number we can have one of the 5 letters. For the third position of serial number we can have one of the 10 numbers. Similarly for the remaining position we can have 9, 8 and 7 possible ways.
So the required number of serial number is
6×5×10×9×8×7=151200
Each serial number of the product consists of six components. First two are letters and remaining four are numbers. So all the serial numbers will look as shown below.
LLNNNN⇑⇑⇑⇑⇑⇑6510987
For the first position of serial number we can have one of the 6 letters. As repetition is not allowed first position of serial number we can have one of the 5 letters. For the third position of serial number we can have one of the 10 numbers. Similarly for the remaining position we can have 9, 8 and 7 possible ways.
So the required number of serial number is
6×5×10×9×8×7=151200
